Asynchronous Locking in Metamaterials of Fluids of Light and Sound

Phonons, the quanta of vibrations, are very important for the equilibrium and dynamical properties of matter. GHz coherent phonons can also interact with and act as interconnects in a wide range of quantum systems. Harnessing and tailoring their coupling to opto-electronic excitations thus becomes highly relevant for engineered materials for quantum technologies. With this perspective we introduce polaromechanical metamaterials, two-dimensional arrays of $\mu$m-size zero-dimensional traps confining light-matter polariton fluids and GHz phonons. A strong exciton-mediated polariton-phonon interaction determines the inter-site polariton coupling with remarkable consequences for the dynamics. When locally perturbed by optical excitation, polaritons respond by locking the energy detuning between neighbor sites at integer multiples of the phonon energy, evidencing synchronization involving the polariton and phonon fields. These results open the path for the coherent control of quantum light fluids with hypersound in a scalable platform.Comment: 31 pages, 19 figure